The present invention relates to data storage, and more particularly, to storing data using partial reverse concatenation that employs composite codes such as product codes and concatenated codes.
Efficient reverse concatenation of composite coding schemes is difficult to achieve. In general, reverse concatenation schemes have several advantages over other data storage techniques. Although reverse concatenation schemes employ large block sizes for modulation coding (MC) in order to achieve a high code rate and improve format efficiency, they do not suffer from error propagation because modulation decoding is performed after error correction coding (ECC) decoding. Moreover, reverse concatenation schemes allow the passing of soft information from the detector to the decoder thereby enabling the use of soft-decoding or iterative decoding techniques to improve error rate performance.
One reverse concatenation architecture for product codes performs conventional reverse concatenation in the sense that it reverses the order of ECC and MC The rate of the modulation code in this approach is 0.9951 whereas the linear tape open (LTO) standard LTO-5 modulation code rate is 32/33=0.9697. Therefore, reversing the order of ECC and MC results in a 2.6% improvement in modulation code rate over the LTO-5 standard, thereby providing a higher tape format efficiency. The modulation code used in the above approach maintains the interleaved (I=11) modulation constraint satisfied in LTO-2 to LTO-5 tape drive standards. However, the G-constraint is weakened from G=14 in LTO-5 to G=22 due to the insertion of parity symbols by the column code which weakens the modulation constraints. Another significant drawback of the reverse concatenation scheme in the above approach is a high implementation complexity which exacerbates the use of this reverse concatenation architecture for product codes in actual practice. The existing reverse concatenation architecture for product codes requires a complete overhaul and redesign of existing data flow architectures which is prohibitively complex when backward compatibility must be provided. In addition to the implementation complexity, another drawback of the above approach is that C2 symbol insertion after MC weakens the achievable modulation constraints. Furthermore, this particular reverse concatenation scheme is not designed to satisfy non-uniform constraints. Therefore, the overall modulation constraints satisfied by this reverse concatenation scheme are not as tight as is desired. For any of these reasons, a system and technique which alleviates the problems associated with conventional reverse concatenation of product coding schemes would be very desirable.